Constrained Motion Class 11 Notes | EduRev

Physics Class 11

Class 11 : Constrained Motion Class 11 Notes | EduRev

The document Constrained Motion Class 11 Notes | EduRev is a part of the Class 11 Course Physics Class 11.
All you need of Class 11 at this link: Class 11

CONSTRAINED MOTION 

1.1 String constraint : 

When the two object are connected through a string and if the string have the following properties :

  • The length of the string remains constant i.e., it is inextensible string
  • Always remains taut i.e., does not slacks.

Then the parameters of the motion of the objects along the length of the string have a definite relation between them.

Ist format : - (when string is fixed) 

Constrained Motion Class 11 Notes | EduRev

The block B moves with velocity v. i.e. each particle of block B moves with velocity v.

If string remain attached to block B it is necessary that velocity of each particle of string is same = v (vs = v)

Now we can say that Block A also moves with velocity v.

Constrained Motion Class 11 Notes | EduRev

  •  : If pulley is fixed then the velocity of all the particles of string is same along the string.

Ex.1

Constrained Motion Class 11 Notes | EduRev 

Sol. In the above situation block B is moving with velocity v. Then speed of each point of the string is v along the string.

speed of the block A is also v

Constrained Motion Class 11 Notes | EduRev

Ex.2 

Constrained Motion Class 11 Notes | EduRev

Sol. Q Block A is moving with velocity 8 ms-1.

velocity of every point on the string must be 8m/s along the string.

The real velocity of B is vB. Then the string will not break only when the compoent of vB along string is 8 m/s.

Constrained Motion Class 11 Notes | EduRev

Constrained Motion Class 11 Notes | EduRev

Ex.3 Find out the velocity of block B in a pulley block system as shown in figure.

Constrained Motion Class 11 Notes | EduRev

Sol. In a given pulley block system the velocity of all the particle of string is let us assume v then.

Constrained Motion Class 11 Notes | EduRev

10 m/s is the real velocity of block A then its component along string is v.

⇒ 10 cos 53° = v ...(1)

If vis the real velocity of block B then it component along string is v then

vBcos37° = v ...(2)

Constrained Motion Class 11 Notes | EduRev

from (1) & (2) vB cos37° = 10 cos53°

Constrained Motion Class 11 Notes | EduRev

Ex.4

Constrained Motion Class 11 Notes | EduRev

What is the velocity of block A in the figure as shown above. 

 

Sol. The component of velocity of ring along string = velocity of A

= Constrained Motion Class 11 Notes | EduRev = vA ⇒ vA = 10 m/s

 

  •  : In the first format only two points of string are attached or touched to moving bodies.


IInd format (when pulley is also moving)

To understand this format we consider the following example in which pulley is moving with velocity vp and both block have velocity vA & vB respectively as shwon in figure.

Constrained Motion Class 11 Notes | EduRev

If we observe the motion of A and B with respect to pulley. Then the pulley is at rest. Then from first format.

vAP = - vBP 

(-ve sign indicate the direction of each block is opposite with respect to Pulley)

Constrained Motion Class 11 Notes | EduRev

  •  : - To solve the problem put the values of vA, vB, & vP with sign.
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